1)
variable exponent \(g(x, {\rm v})= {\rm v}^{\,p(x)-1}\) ,
cf. [1]}, [2]}, [3]},
2)
perturbed variable exponent
\(g(x, {\rm v})= {\rm v}^{\,p(x)-1}\ln (e+{\rm v})\) , cf.
[4]}, [5]}, [6]}, [7]},
3)
double phase \(g(x, {\rm v})= {\rm v}^{\,p-1}+a(x){\rm v}^{\,q-1}\) ,
\(0\leqslant a(x)\in L^{\infty }(\Omega )\) , cf.
[8]}, [9]}, [10]}, [11]}, [12]},
4)
degenerate double phase
\(g(x, {\rm v})={\rm v}^{\,p-1} \big (1+b(x)\ln (1+{\rm v}) \big )\) ,
\(0\leqslant b(x)\in L^{\infty }(\Omega )\) , cf.
[13]}, [9]}, [15]},
5)
double variable exponent
\(g(x, {\rm v})= {\rm v}^{\,p(x)-1}+{\rm v}^{\,q(x)-1}\) ,
cf. [16]}, [17]}, [18]},
6)
variable exponent double phase
\(g(x, {\rm v})= {\rm v}^{\,p(x)-1}+a(x){\rm v}^{\,q(x)-1}\) ,
\(0\leqslant a(x)\in L^{\infty }(\Omega )\) ,
cf. [19]}, [20]}

